Debugging create_mesh, checking influence of mesh density

Whether or not two meshes agree well numerically seems to depend on
how well connected two differently spaced mesh domains are.

@Ternary_model/Ternary_model.m

@@ -36,11 +36,11 @@ classdef Ternary_model < handle
                 T.e_g0 = params(5);
                 T.u_g0 = params(6);
             end
-            T.create_mesh();
+            T.create_mesh(1);
             T.phi_t = Ternary_model.phi_tot(T.x, T.a, T.b, T.e, T.u0);
         end
-        create_mesh(T)
-        plot_sim(T, mode, nth)
+        create_mesh(T, i)
+        plot_sim(T, mode, nth, color)
         solve_tern_frap(T)
         calc_time_scales(T);
     end

@Ternary_model/create_mesh.m

-function create_mesh(T)
+function create_mesh(T, i)
 %CREATE_MESH creates mesh for solving PDE
 %   Mesh density larger for steeper gradients (using inverse of tanh).
 T.x = linspace(-T.a-1, -T.a+1, 3000);
 T.g0 = Ternary_model.gamma0(T.x, T.a, T.b, T.e_g0, T.u_g0);
 g_unique = unique(T.g0);
-x = linspace(g_unique(1), g_unique(end-1), 300);
-g_inv = Ternary_model.spacing(x, T.a, 2*T.b, T.e_g0, T.u_g0);
+x = linspace(g_unique(1), g_unique(end-1), 600);
+g_inv = Ternary_model.spacing(x, T.a, i*T.b, T.e_g0, T.u_g0);
 g_inv = g_inv(2:end-1);
-T.x = [linspace(0, -T.a-0.501, 500), linspace(-T.a-0.5, g_inv(2), 300), g_inv(3:end-2), ...
-    linspace(g_inv(end-1), -T.a+1, 30), ...
-    linspace(-T.a+1.1, T.system_size, 3000)];
+% T.x = [linspace(0, g_inv(5), 300), g_inv(6:end-5), ...
+%     linspace(g_inv(end-4), -T.a+1, 300), linspace(-T.a+1.01, T.system_size, 1000)];
+left = 0:g_inv(8)-g_inv(7):g_inv(7);
+right = g_inv(end-4):g_inv(5)-g_inv(4):-T.a+1;
+T.x = [left, (g_inv(8)+left(end))/2, g_inv(8:end-5), (g_inv(end-5)+right(1))/2, ...
+    right, linspace(-T.a+1.01, T.system_size, 1000)];
 end
 

@Ternary_model/plot_sim.m

-function plot_sim(T, mode, nth)
+function plot_sim(T, mode, nth, color)
 %PLOT_SIM Show movie of simulation
 % mode 'mov' ... show movie
 % mode 'plot' ... show plot
@@ -21,12 +21,12 @@ if strcmp(mode, 'mov')
     %     print([num2str(i),'.png'],'-dpng')
     end
 elseif strcmp(mode, 'plot')
-    figure; hold on;
+%     figure; hold on;
     xlim([0, 2]); ylim([0, 1]);
     ax = gca;
     ax.FontSize = 26;
     xlabel('x [\mum]'); ylabel('volume fraction'); 
-    plot(T.x, T.sol(1:nth:150, :), 'LineWidth', 4, 'Color', [0.5294, 0.8, 0.98]);
+    plot(T.x, T.sol(1:nth:150, :), 'LineWidth', 1, 'Color', color);%[0.5294, 0.8, 0.98]);
     plot(T.x, Ternary_model.phi_tot(T.x, T.a, T.b, T.e, T.u0), 'LineWidth', 6,...
     'LineStyle', '--', 'Color', [0.97, 0.55, 0.03]);
 end

ternary_frap.m

@@ -204,4 +204,26 @@ plot(v_q);
 plot(v_fit')
 figure; hold on;
 plot(sum(v_q));
-plot(sum(v_fit, 2));
\ No newline at end of file
+plot(sum(v_fit, 2));
+%%
+color = ['r', 'b', 'k', 'm', 'y', 'g'];
+figure; hold on;
+wi = [0.1, 0.5, 1.1, 5, 10, 20];
+for i = 1:length(wi)
+% Ts{i} =Ternary_model(2, 'FRAP', [-1, 0.02, 0.5, 0.3, 0.3, 0.5], t);
+% Ts{i}.create_mesh(wi(i));
+% Ts{i}.solve_tern_frap();
+T.create_mesh(i);
+plot(T.x, color(i), 'Marker', '.');
+length(T.x)
+end
+axis([0, 1000, 0, 2])
+%%
+figure; hold on;
+Ts{1}.plot_sim('plot', 10, 'red')
+Ts{2}.plot_sim('plot', 10, 'blue')
+Ts{3}.plot_sim('plot', 10, 'black')
+Ts{4}.plot_sim('plot', 10, 'yellow')
+Ts{5}.plot_sim('plot', 10, 'magenta')
+Ts{end}.plot_sim('plot', 10, 'green')
+xlim([0, 2]); ylim([0, 1]);
\ No newline at end of file